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Infinitely Many Solutions for Systems of Sturm–Liouville Boundary Value Problems

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Abstract

In this paper, the authors obtain the existence of infinitely many classical solutions to the boundary value system with Sturm–Liouville boundary conditions

$$\left\{\begin{array}{ll}-(\phi_{p_i}(u_{i}^\prime))^\prime = \lambda F_{u_{i}}(x,u_{1},\ldots,u_{n})h_{i}(u^\prime_i)\quad {\rm in} \, (a,b), \\ \alpha_iu_{i}(a)-\beta_iu^ \prime_{i}(a)=0, \quad \gamma_iu_{i}(b)+\sigma_iu^\prime_{i}(b)=0, \end{array}\quad{i = 1, \ldots , n.} \right.$$

Critical point theory and Ricceri’s variational principle are used in the proofs.

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA

    John R. Graef & Lingju Kong

  2. Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah, 67149, Iran

    Shapour Heidarkhani

Authors
  1. John R. Graef
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  2. Shapour Heidarkhani
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  3. Lingju Kong
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Correspondence to John R. Graef.

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Graef, J.R., Heidarkhani, S. & Kong, L. Infinitely Many Solutions for Systems of Sturm–Liouville Boundary Value Problems. Results. Math. 66, 327–341 (2014). https://doi.org/10.1007/s00025-014-0379-1

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  • DOI: https://doi.org/10.1007/s00025-014-0379-1

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